https://file.aiquickdraw.com/mathbot/file/1729039798343bg14vpqp.jpg

The question requires you to apply a dilation transformation on the given shape by a factor of \( \frac{1}{4} \), centered at the origin. Here's how dilation works in this context:

1. **Identify Coordinates**: First, take note of the coordinates of the vertices \( J \), \( K \), \( L \), and \( M \) of the shape.
   - Based on the image, you can approximate or directly get the coordinates from the grid.

2. **Dilation Formula**: The dilation of a point \( (x, y) \) centered at the origin by a factor of \( k \) is given by:
   \[
   (x', y') = (k \cdot x, k \cdot y)
   \]
   where \( k \) is the dilation factor, which in this case is \( \frac{1}{4} \).

3. **Apply the Dilation**: Multiply both the x and y coordinates of each vertex by \( \frac{1}{4} \).

### Example:
- If a vertex \( J \) has coordinates \( (-4, -8) \), after dilation, the new coordinates will be:
  \[
  J' = \left( \frac{1}{4} \times (-4), \frac{1}{4} \times (-8) \right) = (-1, -2)
  \]

4. **Plot the New Coordinates**: After finding the new coordinates for all the vertices, plot them on the coordinate plane, and draw the new dilated shape.

If you'd like, I can walk you through each point or clarify any part of the process!

Would you like more details on applying the transformation or solving another example?

### Relative Questions:
1. What are the original coordinates of points \( J \), \( K \), \( L \), and \( M \)?
2. How do you calculate the dilation of a point with a factor other than \( \frac{1}{4} \)?
3. What happens to the shape when a dilation factor is greater than 1?
4. How does a negative dilation factor affect the coordinates and shape?
5. Why does dilation centered at the origin preserve the angles of the figure?

### Tip:
Always ensure that you multiply both x and y coordinates by the same dilation factor to keep the shape proportional.

The figure below is dilated by a factor of 1/4 centered at the origin. Plot the resulting image.

Learn how to perform a dilation transformation by a factor of 1/4 centered at the origin. This example explains step-by-step how to calculate and plot the new coordinates of a figure after dilation. Suitable for students in Grades 8-10.

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